Looking up “draught” in the OED for pronounciation notes, which can’t be copied into here because it’s full of symbols that ordinary HTML can’t render. Apparently the pronounciation “drawt” showed up in late Middle English but went out around the 18th century; the Scots currently pronounce it “dracht” (guttural ch, as in ‘loch’) and everyone else has gone over to “draft,” a pronounciation which the OED editors apparently don’t like because it makes the connection with “draw” less obvious. (A draught is something which is drawn, as a breath, a drink, a pen across a page, or an animal’s load)
The more logical spelling “draft” is therefore coming into use, but is apparently the accepted spelling only for certain senses of the word, e.g. a drafting table, or a gust of wind in a room, and not e.g. a draught of beer or a draught animal.
This has been another useless fact.
Yonatan Zunger’s Blog 
My understanding was that it was simply a difference between British and American English – the English spell it ‘draught’ and we spell it ‘draft’. Interesting.
And at one point thought ‘draught’ was pronounced sort of like ‘drot’. Hehe.
Although in New Zealand (and I would tenatively extrapolate from that to Britain), what we called ‘checkers’ is called ‘draughts’.
Well, if you’re on-campus or somewhere else that has access to the OED online, you can see the gory details here. And it’s a time-varying thing; texts from the 1950’s will talk about a draughtsman making blueprints, for example…
That’s one of those words that the way I pronounce it in my head when I’m reading and the way I say it when I’m speaking have no relationship whatsoever. In my head, I always pronounce it to rhyme with naught. (Of course, I’m also the sort of person that thinks that “ghoti” being pronounced “fish” is humorous.)
I always thought it was pronounced “drout”. Huh. Interesting.
Strange… me too. Which I suppose just puts both of us about 250 years out of date in our heads.
I once failed to convince my high school English class that “draught” was pronounced “draft.” I also failed to convince them that “St. John” is pronounced “Sinjin” when used as a personal name. I don’t know if they ever got that a “gaol” and a “jail” are the same thing.
My mother is a Scot, and I’ve never heard her say “dracht.” I suspect that many pronunciations you see listed as Scots are pretty rare outside the highlands, or are intentionally archaic affectations.